April, 1934
j VALUESOF
THEFREEZING POINTS
THE
SO7
OF A Q U E O U S SOLUTIONS
TABLEI11 TABLE IV ALKALICHLORATES AND PERCHLORATESVALUES FOR -LOG y ’ FOR THE ALKALI CHLORATES AND
Lim. M law KC108 NaClOs 0.001 0.0118 0.0105 0.0110 ,002 ,0167 .0144 .0152 ,005 ,0264 .0221 .0233 .01 .0374 .0308 .0315 .02 .0529 .0435 .0419 .05 .0836 ,0686 .0597 .1 .1182 ,0960 .0761 .2 .1672 .1325 .0958 .3 .2047 a ,1090 .4 .2364 .1195 .5 ,2643 .1285 .6 .2897 .1367 .7 ,3127 ,1445 .8 .3343 .1517 .9 .3546 .1580 1.0 .3738 .1627 1.1 .3920 .1666
LiClOa KC104 NaClOt 0.0109 0.0118 0.0113 .0147 .0168 .0157 ,0216 .0266 .0237 .0284 .0379 .0317 ,0361 ,0539 ,0410 ,0463 ,0579 .0518 .0724 .0513 ,0890 .0459 .0997 ,0381 .lo75 .0292 ,1140 ,0195 .1195 ,0092 .1241 ,0016 .1280 .0125 .1315 .0235 .1344 .0347 .1372
-
-
-
LiClO4 0.0104 .0141 .0204 .0265 .0332 .0417 ,0448 ,0393 ,0277 .0140 - .0006 ,0158 ,0313 .0473 ,0635 .0798 - ,0962
-
Eutectic, M = 0.25148, 8 = 0.79553”, j = 0.1481. Eutectic, M = .04834, 8 = .16353’, j = .0850.
about three hundred-thousandths of a degree for more dilute solutions.a The j values for the chlorates are more negative, that is, the activity coefficients are larger, than those for the corresponding nitrates. Those for lithium and sodium perchlorates are still more negative, so that lithium perchlorate has the most negative j function of any of the twenty-five uniunivalent salts we have studied. The j value for potassium perchlorate is, on the other hand, (3) Earlier measurements are reported only on dilute solutions of sodium and potassium chlorates, and on concentrated solutions of lithium chlorate. The references are given in “International Critical Tables,” Vol. IY, pp. 2588-259.
[CONTRIBUTION FROM
THE
PERCHLORATES M 0.001 .002 .005
.01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8
.9 1.0 1.1
Lim.
law KClOa NaClOa LiCIOa KClOc NaClOl LiCloI 0.0154 0.0142 0.0148 0.0145 0.0154 0.0149 0.0141 .0218 .0196 .0205 ,0201 .0218 .0209 .0194 .0344 .0301 .0316 ,0302 .0347 .0321 .0290 .0487 .0418 .0433 ,0406 .0492 ,0439 .0386 .0689 ,0583 .0588 .0537 ,0697 ,0588 ,0508 .lo89 ,0913 .0866 .0745 .0857 .0892 .1540 .1277 .1139 .0916 .1116 .0835 ,2178 .1771 ,1482 ,1070 .1429 .0940 .2667 a .1718 .1131 .1W ,0948 .3080 .1905 ,1149 .1801 .0914 ,3444 .2066 ,1141 .1936 .0856 .3775 .2203 .1117 ,2052 .0782 ,4074 ,2330 .lo80 ,2151 . O W .4356 .2445 ,1034 .2241 ,0601 .4620 .2551 .0981 .2321 .0501 .4870 .2644 .0923 .2393 .0396 .5107 .2727 .OS60 .2461 .0287
*
’Eutectic, M = 0.25148, -log Eutectic, M = .04834,-log
y’
= 0.1984.
y’ =
.1094.
more positive than those of the chlorate and nitrate, and even more positive than the DebyeHiickel limiting law. The difference from the latter is, however, less than 0.3y0a t the eutectic, and therefore not much more than the error of measurement on this difficultly soluble salt. Except for the “humps” in the curves for the ammonium salts, and the smaller one for lithium chloride, all the uni-univalent salts we have studied fall in the spread of lithium and potassium perchlorates. Their relations will be discussed more fully in paper VI. CAMBRIDGE, MASS.
RECEIVED NOVEMBER 10, 1933
RESEARCH LABORATORY OF PHYSICAL CHEMISTRY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, NO. 3171
The Freezing Points of Aqueous Solutions. VI. Potassium, Sodium and Lithium Formates and Acetates‘ BY GEORGE SCATCHARD AND S. S. PRENTISS The freezing point depressions of the potassium, sodium and lithium formates and acetates were measured since salts of the lower aliphatic acids are of consid.erable practical importance, and because of the information the study of them can give as to the effect of the shape of ions on the properties of their solutions. Aside from the difference between the carbon and nitrogen nuclei, the formate ion differs from the nitrate ion in the replacement of one oxygen by a hydrogen, which decreases greatly the symmetry of the ion, par(1) Paper V i n this series is in THIS JOURNAL, 66, 805 (1984).
ticularly since the ionic charge is doubtless associated with the oxygens. The acetate ion has the additional difference of a CH2 group inserted very unsymmetrically between the carbon and the hydrogen of the formate ion. The lithium formate was prepared from c. P. formic acid and washed lithium carbonate. It was crystallized three times from conductivity water. The starting materials for the other salts were the c. P. or reagent salts. The potassium salts were made neutral to phenolphthalein with c. P. potassium hydroxide. So-
GEORGE SCATCHARD AND S. S. PRENTISS
808
dium acetate was crystallized once, potassium acetate twice, and sodium formate and lithium acetate three times. The stock solutions were all titrated to neutrality with phenolphthalein. The sodium formate was found to contain 0.01% formic acid, a negligible amount, and the others were all neutral. The concentrations were determined by evaporating to dryness with sulfuric acid, igniting (with the addition of ammonium carbonate for each heating of the potassium salts), and weighing as the sulfate. The water and ice were the same as described in paper I. The results of the conductance measurements are given in Table I. M is the concentration in moles per kilogram of water, and L is the specific conductance. The results of the freezing point measurements (calculated by the thermocouple equation of paper IV) are given in Table 11, j is the Lewis and Randall function previously used. The smoothed values of M I L and of j were obtained as in the previous work. Those of j a t round concentrations are given in Table I11 and the corresponding values of -log y’ in Table IV. The average deviation of the experimental points from the smooth curves is about one in the last TABLE I CONDUCTANCE AT 10 M
M/L KOOCH
1.2921 0.90128 .65673 .49158 ,31413 ,28078 ,17904 ,071753 ,044195 ,023248 ,007505 ,003317 ,000895
16.438 15.538 14,926 14,468 13,887 13.763 13.301 12.582 12,276 11.946 11.527 11.206 11,132
KOOCCHs
1,4472 1.2531 0.95623 ,82995 ,58354 ,45884 ,32130 ,22671 ,19485 .18129 .081949 .053949 .022410 .008787 ,003775 .001065
22.179 21 192 19.703 19,079 17.828 17.166 16.382 15 777 15.550 15,446 14.537 14.171 13.622 13.236 12.936 12.727
M
MIL
NaOOCH
1.3037 1.1619 1.0461 0.89848 ,68334 ,56892 .41634 ,24015 ,17240 ,10929 ,068365 .042924 ,014023 ,008526 ,003022 .001233
24,767 23,928 23,247 22,381 21,122 20.394 19.387 18.055 17.436 16.737 16,139 15,703 14.888 14,637 14.241 14.043
NaOOCCHt 1 ,4240 35,276 1.1182 31.740 1.0414 30.890 0.87194 29.041 .71627 27.382 ,50459 23.756 ,39003 23.830 ,27943 22,524 ,23777 21.999 ,17415 21.127 .lo602 20.042 ,069812 19.334 .024871 18.071 ,013542 17.562 ,004673 16,937 ,001722 16.590
O
M
M/L
LiOOCH
1.2902 1.1834 1.1434 1.0071 0.81478 ,61969 ,47293 ,34701 ,24383 ,11871 ,071090 ,024485 ,017320 .005615 ,001939
35.652 34.254 33.733 31.987 29.568 27,127 25.265 23.588 22,102 19.991 18.961 17.532 17.208 16.461 16.065
LiOOCCHt
1.2893 1.1382 1.0086 0.82661 ,74936 .66864 ,54821 .45620 ,38737 ,27167 ,14643 ,10218 ,063608 ,032220 ,012701 .004611 ,001897
51.284 47,608 44,600 40,522 38,855 37.134 34,585. 32.630 31,182 28,646 25.622 24,351 23.089 21.759 20.552 19,747 19.318
Vol. 56
place given for M/L, about 0.06% f o r j in solutions more concentrated than 0.01 M , and about four hundred-thousandths of a degree for the more dilute solutions.2 The acid dissociation constant of acetic acid is almost exactly equal to the basic dissociation constant of ammonia. Therefore the calculation of the effect of hydrolysis on the freezing points given in paper 1113may be applied equally well to the acetates. The effect is negligible in the range of our experiments for the salts of acetic acid, and is even smaller for the salts of the stronger formic acid.
Discussion The behavior of the formates and acetates is quite different from that of the halides or that or* the nitrates, chlorates and perchlorates. For the acetates the osmotic coefficient (1 - j ) increases in the order : lithium, sodium, potassium, while for the salts previously studied the osmotic coefficients decrease in that order. The spread of the formates is not very great but the order is the same as for the acetates below 0.4 M . Above that concentration the coefficient of sodium formate is smaller than that of the lithium salt. We have completed measurements of the freezing point depressions of twenty-five uniunivalent salts, and shall now attempt to correlate the results with the size and structure of the ions. The mass of data is too large to make comparisons a t all concentrations, and it is necessary to make some arbitrary choice. If we were to limit the discussion to our own measurements we should choose the term proportional to the concentration determined from dilute solutions in a previous paper.4 However, we find it desirable to include measurements on other electrolytes, generally less accurate than our own, and shall therefore compare the osmotic coefficients (1 - j ) in one molal solutions. We include in our discussion the results on other alkali halides summarized by Fajans5 largely from measurements in his laboratory, and those on the alkali hydroxides and on the acids corresponding to the salts included.6 (2) Earlier measurements have been reported only for potassium and sodium acetates. The references are given in “International Critical Tables,” Vol. IV, pp. 258-259. (3) THISJOURNAL, 64,2696 (1932). (4) Prentiss and Scatchard, Chcm. Reviews, 18, 139 (1933). (5) Fajans and Karagunis, Z. angew. Chcrn., 48, 1046 (1930); Fajans, “Chemistry at the Centenary (1931)Meeting of the British Association for the Advancement of Science,” W. Heffer and Sons Cambridge, 1931,p. 49. ( 6 ) From “International Critical Tables,” Vol. IV, pp 258-282.
809
THEFREEZING POINTS OF AQUEOUS SOLUTIONS
April, 1934
TABLE 11 FREEZING POINTS ’$1
M
M
j
KOOCH E F B E F E F
0.28357 ,34072 .38232 ,40356 ,43592 .49297 .53850
0.0713 ,0723 .0730 .0718 ,0719 ,0712 .0705
E F E F E F E
0.60476 ,67506 ,75393 .84394 .94757 1.0804 1.1935
0.0693 ,0677 .0659 ,0635
E B I? E F E F
0.36013 .40i96 ,44735 ,51583 ,55167 ,62615 .67822
0.0796 ,0802 .0805 .0812 .OH3 .0819 .0824
E F E F E F E
0.75667 .82372 ,92520 ,99886 1.1171 1.2181 1.3908
0.0826 0x09 ,0792 ,0782 ,0777 ,0753 ,0731
0.054475 .Oi8905 .11198 .I3446 .17683 .22410 .26664
LiOOCH E 0.0566 , oti2(i F . OR83 B ,0704 E F ,0745 ,0776 E .0788 F
0.31184 .37923 ,41849 ,46309 ,50752 ,56314 .62556
0.0799 .0799 .Of300 ,0799 ,0791 ,0786 ,0766
E F E F E
0.69146 ,76218 .&I182 .92016 1.0297 1.1275 1.2701
0.0754 ,0736 .0718 ,0689 ,0666 ,0626 ,0599
0,028042 ,039445 ,041614 .057889 .Om71 ,10750 .14223 .18446
KOOCCH3 0.0410 B .0415 I’ A .0424 ,0463 F .0487 E ,0510 €3 .0510 1’ .0504 E
0.22112 .26739 ,31223 .34622 ,36908 .40614 .45150 .51303
0.0483
0,049766 ,054054 .Om874 .111456 .13560 ,15614 .18475 .21264
NaOOCCHa 0.0472 I; .0467 Is ,0509 13 ,0522 E F’ .0534 . 0535 E .0537 F .0534
0.23726 .27632 .32031 .39975 ,43636 .50946 .56806
0.0517 ,0504 ,0486 .0425 ,0406 ,0353 .0312
0 . 0492
0.000893 ,002286 ,006046 ,010704 .016438 .021241 ,029945
0 0145 .008X .0247 .0273 .0:331 .OK32 ,0425
B A B A B F
A
0.046477 ,088190 ,093846 ,11777 .15410 .I9065 .22630
0.001668 .OO3OOG .005921 ,009982 .016956 .026497 .037668 .059993
0 0094 .ON8 .0201 .0297 .0343 ,0454 ,0470 .0562
A B A B F A F
0.077829 .lo800 .13371 ,17117 .21066 .25405 .30328
NaOOCH O.O(j00 ,0843 .0674 .0711 ,0729 ,0764 .0781
A B A B A B A
0.001661 ,003859 .006142 .0105i’7 .014980 .025351 ,037415
G1.0555
B
,0185 .0234 .0315 .0348 ,0460 ,0508
A B A B F A
A
4
B A B C
0.000577 -G I.0024 .0153 .0020t;1 ,0233 ,002072 ,0102 .003866 ,0213 .005497 ,0302 ,00841.3 ,0342 ,015280 ,0455 .021154 ,0386 ,021647
A B A B A B A B
0.000682 ,0022 14 ,002879 ,005805 ,007657 015628 ,023479 ,037656
0091
.4
02.52 0167 0256 0251 0335 0417 0447
B A B A F B A
A B A
B A B A
c B A
c
+
13
B C A B A B A
,0561 ,0008 ,0639 .0672 ,0698 .070G
F
E
.0605 ,0567 .0525
I
0.56263 0 0181 ,62838 ,0109 .69829 0039 ,77783 - 0052 ,85618 - ,0131 94916 - 0237 1 0509 - 0347 1.1606 - 0478
.OM8 .0420 .0388 ,0366 .0338 .0291 .0230
E F E F E F E
0 65213 0 0251 .71788 0201 ,79685 ,0134 ,90198 0033 .98834 - 0026 1 0602 - 00!).3 1 2347 - 0208
LiOOCCH3 E 0.70398 0.0352 E 0.23233 0.0627 B 0.055988 0.0525 0 0267 F ,77000 ,0294 .0606 ,0565 F .28437 A .082635 .0206 .0611 E .%I652 ,0238 .0598 €3 .31092 B .lo681 ,0259 F ,92291 0176 E ,38568 .0565 . Mil5 A .13449 ,0308 R E 1.0080 ,0102 .0515 ,0644 F ,46963 B .I6783 x 0319 ,0455 F 1 0588 ,0067 0636 E .56001 F .18282 B ,0424 E 1.1965 - ,0077 1: .61701 .0411 . O(i33 A ,21374 ,0467 H ..\ .0493 The letters denote the sei-ies. Series A-D we1-e run with increasing concentrations and sei-ies E-H with decreasing concentrations. A R A
0.001842 .002253 .006059 ,010535 .0151!% ,0231154 ,0334i9 ,0396’77
810
GEORGE SCATCHARD AND S. S. PRENTISS
TABLE I11 AND ACETATES j VALUESOF THE ALKALIFORNATES
Vol. 56
cient increases for the lithium and sodium salts and decreases for the cesium salts; the salts of Lim. KONaLiKONaOLiOpotassium show a flat minimum at the chloride; M law OCH OOCH OOCH OCCHa OCCHs OCCHI 0.001 0.0118 0.0108 0.0110 0.0111 0,0109 0.0110 0,0110 the difference between rubidium chloride and ,0148 .0149 .0151 .M)2 .OM7 .0146 .0150 .0150 fluoride is intermediate between those of the .0220 ,0220 .0226 ,005 .0264 .0216 ,0222 .0228 .0374 ,0286 ,0295 .0304 ,0289 .0288 .0301 .01 corresponding potassium and cesium salts; ru.0529 ,0371 ,0383 .0402 .0366 .0365 ,0391 * 02 bidium bromide and iodide have not been meas,0836 ,0505 ,0519 ,0552 .0463 .0468 ,0517 .05 .0509 .0526 ,0597 ,1182 ,0616 ,0629 ,0665 .1 ured. These relations may be explained theo,1672 ,0697 ,0732 ,0761 ,0492 .0531 ,0631 .2 retically by including the three types of inter,2047 .0721 ,0779 .0796 ,0427 .0490 .0606 .3 .2364 ,0721 ,0802 ,0802 ,0340 ,0431 ,0559 .4 action : charge-charge, charge-molecule, molecule.0244 ,0364 ,0498 ,2643 .0711 .OS13 .0793 .5 molec~le.~ ,2897 ,0694 .OS16 ,0776 .0142 .0290 ,0428 .6 ,3127 ,0671 ,0813 .0751 ,0036 ,0210 ,0353 .7 These variations in behavior of the symmetrical ,0131 ,0274 ,3343 ,0646 .OS07 .0727 - .0071 .8 ions show clearly that any consideration of the .0048 .0192 .3546 ,0619 .0799 .0698 - .0181 .9 .3738 .0589 ,0788 .0671 - .0292 - ,0038 .0105 1 .o effect of dissymmetry must take into account the ,3920 ,0578 .0775 ,0642 - .0404 - .0126 .0017 1.1 sizes of the ions. The radii of the alkali and TABLE IV halide ions may be determined from studies of VALUESFOR -LOG y’ FOR THE ALKALIFORMATES AND crystal structure, but the method cannot be ACETATES extended to the polyatomic ions. As a rough Lim. NaLiKONaOLiOM law KOOCH OOCH OOCH OCCHa OCCHa OCCHs measure of the relative size of the cations we shall 0,001 0.0164 0.0145 0.0146 0.0147 0.0146 0.0146 0 0146 take the apparent molal volume of the chloride in .002 ,0218 .0199 .0203 .0204 .0201 .0203 .0204 one molal solution a t Bo, and for the anions we ,006 ,0344 .0302 .0308 ,0311 .0306 .0306 ,0309 .01 .0487 .0406 .0416 .0424 ,0411 .0412 .0421 shall take the apparent molal volume of the .02 ,0689 .0543 .0557 ,0673 .0544 ,0544 .0564 sodium salt under the same conditions.s Any .05 ,1089 ,0774 .0794 .OS28 .0760 .0754 .0799 .1 .1540 .0989 .lo12 ,1057 ,0915 ,0928 .lo00 other choice of accompanying ion or of conditions .2 .2178 .1221 .1262 ,1312 .lo61 ,1089 .1201 would probably lead to slightly different relative .3 ,2867 .1356 .1416 .1465 .1113 .1160 ,1298 .4 .3080 ,1445 .1522 .1565 ,1122 .1192 .1349 values. Our choice was determined by the fact .5 .3444 .1509 ,1606 .1637 .1107 .1199 .1373 that measurements are thus available for all the .6 .3778 .1556 .1669 .1692 .lo76 .1191 .1379 .7 .4074 .1589 ,1720 .1729 .lo34 .I172 ,1370 ions. .8 .4356 ,1616 ,1763 .1761 .0986 .1156 .1353 Table V shows the osmotic coefficients of these .9 .4620 ,1635 .1799 .1783 ,0928 .1112 .1329 1.0 ,4870 .1648 .1829 .1802 .OS67 .lo74 .12Y6 electrolytes. Below each cation is the apparent 1.1 ,5107 .1674 .1854 .1814 .OS04 ,1029 .1257 molal volume of its chloride, and after each TABLE V anion is that of its sodium salt (in parentheses). OSMOTICCOEFFICIENTS OF UNI-UNIVALENT ELECTROLYTES The ions are arranged in increasing order of these AT ONE MOLAL (APPARENTMOLALVOLUMES IN PARENvolumes, except the sodium and lithium ions for THESES) which it contradicts the sizes from crystal strucLi Na K Rb OH8 NH, Cs (18.4)(17.9)(28.4)(33.5)(36.8)(37.2)(40.7) ture. For the acids the values given in the literaO H (-3.1) 0.89 0.93 0.97 ture are molal depressions of H X a t 1.0 M H X or F (-0.6) 8 S 0.90 0.94 0.51 1 01 (17.9) 1.09 0 . 9 1 C1 .88 .8S 1.04 0.89 0.82 1.018 M OH& The values in the table are 1.06 .94 .88 1.06 .89 .81 (24.6) Br computed from the molal depressions of OH3X a t 0.93 .92 .94 Fo (26.4) 0.48 (29.8) 1.00 .81 .69 NOa .95 .79 this concentration, and are not very different from I (35.5) >1.10 .99 .91 1.08 .90 s the values at 1.0 M OH&. The alkali halides are (37.2) C103 1.02 .84 S 0.47 (41 3) 0.90 1.00 1.03 Ac printed in heavy type. For certain salts measClOi (45.7) 1.08 0.87 S urements are available only a t concentrations Fajans found that, even with the noble gas type smaller than 1.0 M , generally on account of the ions, the osmotic coefficient is a complicated limited solubility. These all have small osmotic function of the sizes of the two ions. We may coefficients, smaller than those of their neighbors sum up qualitatively the findings of Fajans as on any side. They are marked S in the table. follows: with increasing atomic number of the There is not enough variety in the polyatomic cation, the osmotic coefficient increases for the cations to show very much. The large, tetrafluorides and decreases for the other halides, and (7) Scatchard, Chcm. Rcoicws, 13, 7 (1933); Scatchard and Allen, the decrease is greater the larger the anion; with unpublished. (8) From densities in the “International Critical Tables,” Vol. increasing atomic number of the anion, the coeffi- 111, pp, 51-95.
THEFREEZING POIN%OF AQUEOUSSOLUTIONS
April, 1934
811
hedrally symmetrical ammonium ion behaves like fluoride ion and that of the neutral tail. The a much smaller noble gas type ion, intermediate dissymmetry of the hydroxide ion is so small that between sodium and potassium. There is in it might be expected to behave almost as the addition the hump (negative in the osmotic fluoride ion, and its behavior may be attributed coefficient) in dilute solutions which appears mostly to its small size. characteristic of the ammonium salts3 The The behavior of the second class-nitrate, strong acids behave very much as the lithium salts chlorate and perchlorate-is more difficult to in spite of the large difference in size between the explain. We have succeeded only in eliminating “oxonium” and lithium ions In the weak acids certain factors. The fact that the behavior is HX HnO is directly opposite to that of the acetates shows the equilibrium (OHs+ Xdoubtless involved, so that we should not expect that it cannot be explained by a charge near the them to fall into our classification. It may be surface. The fact that the difference from the noted, however, that extrapolation to a volume halide ions is no greater for the chlorate, which corresponding to that of the proton would give an should have a dipole, than for the nitrate and effect in the right direction. perchlorate, which have no dipoles unless the The anions may be divided into three classes, structure in solution is very different from that in The first of these is made up of the halides, and the crystal, eliminates the dipole moment as an may be taken as the norm since the ions are all important factor. It may be that the higher spherically symmetrical. In the second class the moments, produced by the first loss of spherical coefficient of the lithium salt is smaller than that symmetry, are important factors; or it may be of a halide ion of the same volume, and the de- that the fact that the surface of these ions is crease with increasing volume of the cation is largely made up of doubly bound oxygen atoms is faster. This class includes the nitrates, chlorates of importance. It appears that a large amount of and perchlorates. The third class shows a less additional data will be necessary to give a closer rapid decrease, or a more rapid increase, than a insight into this problem. halide ion of the same volume. The acetate ion is Summary the most marked as it shows qapid increase in The freezing point depressions of lithium, spite of its large volume, and the formate ion is sodium and potassium formates and acetates have also distinctly in this class; the hydroxide ion been measured up to concentrations a little appears to be on the border line between this greater than one molal. class and that of the halide ions. The doubt The measurements obtained in this Laboratory arises largely from the lack of knowledge about on twenty-five uni-univalent electrolytes and the fluorides of small cations. many other data are correlated. The polyatomic There is little question but that the third class anions are divided into two classes which deviate is the one which shows the effect of concentration in opposite ways from the noble gas type ions. of the ionilc charge far from the mechanical center The deviations of the formates and acetates are of the ion. Such an ion might be expected to be explained by the concentrations of the ionic roughly equivalent to a much smaller symmetrical charge near the surface. For the nitrates, ion, plus :i neutral tail which should give an inchlarates and perchlorates we cannot do more a t crease in the osmotic coefficient especially for present than eliminate this effect and the presence small cations. ‘The behavior of the acetates and formates may in fact be calculated approximately of a dipole as important factors. MASS. RECEIVED NOVEMBER 10, 1933 by summing that of an ion about the size of the CAMBRIDGE,
+
+
